It could be broken.
Is there a smaller panel that the power button is attached to that can be pried off? Some cases have an inner panel under the power button, with a short wire running from the power button to that panel that isn't connected when the case ships. The normal cord that runs from the power button to the motherboard is connected to the other side of that inner panel. If you just plug that into the motherboard, the system won't power on because the power button isn't actually connected yet.